Finite Group Databasebeta

← #15772096

Subgroups — #15772096

Order 3328.

562 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 562 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13117448C211yesmaximal, characteristic
2C2×#11718117C211yesmaximal, characteristic
3#13112785C212yesmaximal, complemented
4#13112783C212yesmaximal, complemented
5C2×C13×#323C211yesmaximal, characteristic
6C22×C13×C22⋊C4C2211yescharacteristic
7C22×C22⋊Dic13C411yescharacteristic
8C22×C22⋊Dic13C411yescharacteristic
9C2×C13×C22⋊C8—21no—
10#11718871—21no—
11#11718871—21no—
12C2×C22⋊#1055—21no—
13#11718607C411yescharacteristic
14#11718607C411yescharacteristic
15#11718607C2211yescharacteristic
16#11718607C2211yescharacteristic
17#11718603—21no—
18#11718603—21no—
19C13×#323—21no—
20C13×#323C2212yes—
21#11718117—21no—
22#11718117C2212yes—
23C25×C13C2×C411yescharacteristic
24C23×C4×C13D411yescharacteristic
25C23×C4×C13D411yescharacteristic
26C23×Dic13—21no—
27C23×Dic13C2×C411yescharacteristic
28C23×Dic13C2×C411yescharacteristic
29C22×C8×C13—41no—
30C2×C13×C22⋊C4—41no—
31C2×C13×C22⋊C4—41no—
32C2×C13×C22⋊C4C2×C411yescharacteristic
33C2×C13×C22⋊C4D411yescharacteristic
34C2×C13×C22⋊C4D411yescharacteristic
35C2×C13×C22⋊C4C2311yescharacteristic
36C2×C22⋊Dic13—21no—
37C2×C22⋊Dic13—22no—
38C2×C22⋊Dic13—21no—
39C2×C22⋊Dic13—21no—
40C2×C22⋊Dic13—41no—
41C2×C22⋊Dic13—41no—
42C2×C22⋊Dic13C814yescomplemented
43C2×C22⋊Dic13C2×C411yescharacteristic
44C2×C22⋊Dic13C2×C411yescharacteristic
45C2×#6101—21no—
46C2×#6101—21no—
47C2×#6101—21no—
48C2×#6101—21no—
49C22×#1055—41no—
50C13×C22⋊C8—22no—
51C13×C22⋊C8—41no—
52#88071—21no—
53#88071—21no—
54#88071—21no—
55#88071—21no—
56C22⋊#1055—22no—
57C22⋊#1055—41no—
58#11453—131nomaximal, Sylow
59C24×C13—21no—
60C24×C13—21no—
61C24×C13—22no—
62C24×C13—81no—
63C24×C13—81no—
64C24×C13C22⋊C411yescharacteristic
65C24×C13C22⋊C411yescharacteristic
66C24×C13C2×C812yes—
67C24×C13M1612yes—
68C24×C13C22×C411yescharacteristic
69C22×C4×C13—21no—
70C22×C4×C13—21no—
71C22×C4×C13—21no—
72C22×C4×C13—21no—
73C22×C4×C13—81no—
74C22×C4×C13—81no—
75C22×C4×C13C22⋊C411yescharacteristic
76C22×C4×C13C22⋊C411yescharacteristic
77C22×C4×C13C2×D411yescharacteristic
78C22×C4×C13C2×D411yescharacteristic
79C22×Dic13—21no—
80C22×Dic13—21no—
81C22×Dic13—24no—
82C22×Dic13—21no—
83C22×Dic13—21no—
84C22×Dic13—41no—
85C22×Dic13—41no—
86C22×Dic13—81no—
87C22×Dic13—81no—
88C22×Dic13—81no—
89C22×Dic13—81no—
90C2×C8×C13—42no—
91C2×C8×C13—82no—
92C13×C22⋊C4—41no—
93C13×C22⋊C4—41no—
94C13×C22⋊C4—41no—
95C13×C22⋊C4—41no—
96C22⋊Dic13—24no—
97C22⋊Dic13—21no—
98C22⋊Dic13—21no—
99C22⋊Dic13—42no—
100C22⋊Dic13—41no—
101C22⋊Dic13—41no—
102C22⋊Dic13C2×C812yescomplemented
103C22⋊Dic13C2×C812yescomplemented
104#6101—81no—
105#6101—81no—
106#6101—81no—
107#6101—81no—
108C2×#1055—42no—
109C2×#1055—82no—
110#2315—131no—
111C2×#323—131no—
112C2×#323D1311yescharacteristic
113#1326—132no—
114#1326—132no—
115C23×C13—21no—
116C23×C13—21no—
117C23×C13—21no—
118C23×C13—21no—
119C23×C13—22no—
120C23×C13—22no—
121C23×C13—22no—
122C23×C13—22no—
123C23×C13—41no—
124C23×C13—41no—
125C23×C13—41no—
126C23×C13—41no—
127C23×C13—41no—
128C23×C13—41no—
129C23×C13—81no—
130C23×C13—81no—
131C23×C13—81no—
132C23×C13—81no—
133C23×C13—84no—
134C23×C13—82no—
135C23×C13—82no—
136C23×C13C22⋊C812yes—
137C23×C13C22⋊C812yes—
138C23×C13#9911yescharacteristic
139C23×C13#9911yescharacteristic
140C23×C13#10112yes—
141C23×C13C2×C22⋊C411yescharacteristic
142C23×C13C22×C811yescharacteristic
143C23×C13C2×M1611yescharacteristic
144C2×C4×C13—21no—
145C2×C4×C13—21no—
146C2×C4×C13—21no—
147C2×C4×C13—21no—
148C2×C4×C13—42no—
149C2×C4×C13—42no—
150C2×C4×C13—41no—
151C2×C4×C13—41no—
152C2×C4×C13—41no—
153C2×C4×C13—41no—
154C2×C4×C13—81no—
155C2×C4×C13—81no—
156C2×Dic13—22no—
157C2×Dic13—22no—
158C2×Dic13—41no—
159C2×Dic13—41no—
160C2×Dic13—41no—
161C2×Dic13—41no—
162C2×Dic13—41no—
163C2×Dic13—41no—
164C2×Dic13—41no—
165C2×Dic13—41no—
166C2×Dic13—41no—
167C2×Dic13—41no—
168C2×Dic13—84no—
169C2×Dic13—82no—
170C2×Dic13—82no—
171C8×C13—82no—
172#1055—82no—
173C22×C22⋊C4—131no—
174C22×C22⋊C4—131no—
175C22×C22⋊C4C2×D1311yescharacteristic
176C2×C22⋊C8—21no—
177C2×C22⋊C8—261no—
178#385—131no—
179#385—131no—
180#385—131no—
181#385—131no—
182#385—261no—
183#385—261no—
184#380—261no—
185#380—261no—
186#323—21no—
187#323—132no—
188#323—261no—
189#323C2×D1312yes—
190C22×C13—21no—
191C22×C13—21no—
192C22×C13—21no—
193C22×C13—21no—
194C22×C13—21no—
195C22×C13—21no—
196C22×C13—22no—
197C22×C13—21no—
198C22×C13—21no—
199C22×C13—42no—
200C22×C13—42no—
201C22×C13—42no—
202C22×C13—41no—
203C22×C13—41no—
204C22×C13—42no—
205C22×C13—42no—
206C22×C13—41no—
207C22×C13—41no—
208C22×C13—41no—
209C22×C13—41no—
210C22×C13—82no—
211C22×C13—82no—
212C22×C13—82no—
213C22×C13—82no—
214C22×C13#32412yes—
215C22×C13#32412yes—
216C22×C13C2×C22⋊C811yescharacteristic
217C22×C13C2×#9911yescharacteristic
218C22×C13C2×#10111yescharacteristic
219C4×C13—41no—
220C4×C13—41no—
221C4×C13—41no—
222C4×C13—41no—
223Dic13—42no—
224Dic13—42no—
225Dic13—81no—
226Dic13—81no—
227C25C4×D1311yescharacteristic
228C23×C4—131no—
229C23×C4—131no—
230C23×C4—261no—
231C23×C4D5211yescharacteristic
232C23×C4C22⋊D1311yescharacteristic
233C22×C8—41no—
234C22×C8—521no—
235C2×C4⋊C4—261no—
236C2×C4⋊C4—261no—
237C2×C4⋊C4—261no—
238C2×C4⋊C4—261no—
239C2×C22⋊C4—41no—
240C2×C22⋊C4—41no—
241C2×C22⋊C4—134no—
242C2×C22⋊C4—131no—
243C2×C22⋊C4—131no—
244C2×C22⋊C4—262no—
245C2×C22⋊C4—261no—
246C2×C22⋊C4—261no—
247C2×C22⋊C4—261no—
248C2×C22⋊C4—521no—
249C2×C22⋊C4—521no—
250C2×C22⋊C4C4×D1311yescharacteristic
251C2×C22⋊C4D5211yescharacteristic
252C2×C22⋊C4C22⋊D1311yescharacteristic
253C2×C22⋊C4C22×D1311yescharacteristic
254C22⋊C8—22no—
255C22⋊C8—41no—
256C22⋊C8—262no—
257C22⋊C8—521no—
258#95—261no—
259#95—261no—
260#95—261no—
261#95—261no—
262C2×C13—21no—
263C2×C13—21no—
264C2×C13—22no—
265C2×C13—22no—
266C2×C13—42no—
267C2×C13—41no—
268C2×C13—41no—
269C2×C13C2×#32411yescharacteristic
270C2×C13#212111yescharacteristic
271C2×C13#212111yescharacteristic
272C24—22no—
273C24—21no—
274C24—21no—
275C24—81no—
276C24—81no—
277C24C8×D1312yes—
278C24#609412yes—
279C24#610311yescharacteristic
280C24#610311yescharacteristic
281C24C2×C4×D1311yescharacteristic
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—81no—
287C22×C4—81no—
288C22×C4—261no—
289C22×C4—261no—
290C22×C4—264no—
291C22×C4—261no—
292C22×C4—261no—
293C22×C4—521no—
294C22×C4—521no—
295C22×C4—1041no—
296C22×C4—1041no—
297C22×C4—1041no—
298C22×C4—1041no—
299C22×C4#610311yescharacteristic
300C22×C4#610311yescharacteristic
301C22×C4C2×D5211yescharacteristic
302C22×C4C2×C22⋊D1311yescharacteristic
303C2×C8—42no—
304C2×C8—82no—
305C2×C8—522no—
306C2×C8—1042no—
307C4⋊C4—1041no—
308C4⋊C4—1041no—
309C4⋊C4—1041no—
310C4⋊C4—1041no—
311C22⋊C4—41no—
312C22⋊C4—41no—
313C22⋊C4—41no—
314C22⋊C4—41no—
315C22⋊C4—132no—
316C22⋊C4—132no—
317C22⋊C4—261no—
318C22⋊C4—261no—
319C22⋊C4—264no—
320C22⋊C4—522no—
321C22⋊C4—521no—
322C22⋊C4—521no—
323C13#1145311yescharacteristic, complemented, Sylow
324C23—21no—
325C23—21no—
326C23—21no—
327C23—21no—
328C23—22no—
329C23—22no—
330C23—22no—
331C23—22no—
332C23—41no—
333C23—41no—
334C23—41no—
335C23—41no—
336C23—41no—
337C23—41no—
338C23—81no—
339C23—81no—
340C23—81no—
341C23—81no—
342C23—82no—
343C23—82no—
344C23—84no—
345C23#8804611yescharacteristic
346C23#8804611yescharacteristic
347C23#8806012yes—
348C23#8806012yes—
349C23#8806412yes—
350C23C2×C8×D1311yescharacteristic
351C23C2×#609411yescharacteristic
352C23C2×#610311yescharacteristic
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—81no—
364C2×C4—81no—
365C2×C4—262no—
366C2×C4—262no—
367C2×C4—521no—
368C2×C4—521no—
369C2×C4—521no—
370C2×C4—521no—
371C2×C4—521no—
372C2×C4—521no—
373C2×C4—521no—
374C2×C4—521no—
375C2×C4—521no—
376C2×C4—521no—
377C2×C4—1044no—
378C2×C4—1042no—
379C2×C4—1042no—
380C8—82no—
381C8—1042no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—22no—
391C22—42no—
392C22—42no—
393C22—42no—
394C22—41no—
395C22—41no—
396C22—42no—
397C22—42no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—82no—
403C22—82no—
404C22—82no—
405C22—82no—
406C22#1171806112yes—
407C22#1171806112yes—
408C22C2×#8804611yescharacteristic
409C22C2×#8806011yescharacteristic
410C22C2×#8806411yescharacteristic
411C4—41no—
412C4—41no—
413C4—41no—
414C4—41no—
415C4—522no—
416C4—522no—
417C4—1041no—
418C4—1041no—
419C2—21no—
420C2—21no—
421C2—22no—
422C2—22no—
423C2—41no—
424C2—41no—
425C2—42no—
426C2C2×#1171806111yescharacteristic
427C2#1311648011yescharacteristic
428C2#1311648311yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC23×C13C22×C8
FrattiniC2×C22⋊C4C22×D13
FittingC2×C13×#323C2
socleC22×C13C2×#99
prime radicalC25×C13C2×C4
cosocleC2×C13×C22⋊C4C23
hypercenterC2×#323D13
hypocenterC13#11453
LCSG ▷ C23×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C24 ◁ C22×C22⋊C4 ◁ C2×#323

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. #13112785C2semidirect
4. #13112783C2semidirect
42. C2×C22⋊Dic13C8semidirect
102. C22⋊Dic13C2×C8semidirect
103. C22⋊Dic13C2×C8semidirect
323. C13#11453semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#131174482
C2×#117181172
#131127852
#131127832
C2×C13×#3232
#1145313